Personal income inequality and aggregate demand∗

Laura Carvalho†

Armon Rezai‡

Abstract

This paper presents a theoretical and empirical investigation of how changes in thesize distribution of income can affect aggregate demand and the demand regime of aneconomy. After presenting empirical evidence for the US economy that the propensityto save increases significantly from the bottom to the top quintile of wage earners, wedemonstrate that more equal distributions always lead to higher output in the traditionalneo-Kaleckian macroeconomic model. We also present conditions under which a re-duction of income inequality among workers turns demand more wage-led. This viewis supported by the results of an econometric study for the United States (1967-2010)which show that the rise after 1980 in income inequality has made the US economymore profit-led.

Keywords: Income inequality, demand regimes, Neo–Kaleckian model, personal andfunctional income distribution.

JEL classification numbers: D31, E25, C32

Area 4: Macroeconomics, Monetary Economics and Financial Economics

∗We benefited from comments by Lance Taylor. Armon Rezai thanks the Sao Paulo School of Economicsfor its hospitality. The usual disclaimer applies.

†Sao Paulo School of Economics - FGV. Corresponding author: laura.carvalho@fgv.br.‡Vienna University of Economics and Business, Institute of Socio-Economics

1 IntroductionAs the unprecedentedly large share of income held by the top 1% was incorporated into theslogan of the Occupy Wall Street movement, the substantial rise in income inequality in theUnited States since the 1970s became acknowledged by a wider public. In the economic lit-erature, the main reference for this topic is Piketty and Saez (2003) who compile a series forthe top shares of income and wages from 1913 to 1998 to conclude that income inequality hasnot only been increasing as a whole in the recent decades, but also that the working rich havereplaced the rentiers at the top of the US income distribution. Palma (2011) extends the em-pirical analysis to a large number of countries and shows that inequality within countries hasbeen the major cause of the global trend in income inequality in the past decades. One pos-sible explanation for this pattern can be found in the work by Mohun (2012), which presentsevidence of an increase in the share of supervisory workers in total wages. This phenomenonserves as main motivation for this paper which aims at studying the implications of a risinginequality among wage earners for aggregate demand and its relationship to functional in-come distribution. The proponents of the Occupy Wall Street movement have, among otherthings, called for reform of the tax system to reduce income inequality. Our theoretical andempirical work traces through the generally positive macroeconomic implications of suchpolicy proposals.

The macroeconomic effects of changing the functional distribution of income has beeninvestigated extensively in both the theoretical and empirical economic literature. AlreadyKeynes (1936) recognized the distributive effects on demand, e.g. in his condemnation ofhigh-saving rentiers and bear speculators. Kaldor (1955) first formalized the idea that sav-ings propensities are different between profit earners and wage earners making aggregatedemand sensitive to a redistribution of income. This assumption has then been combinedwith Kaleckian mark-up pricing (Kalecki, 1971) and an independent investment function inthe so-called Neo-Kaleckian models developed seminally by Rowthorn (1982), Dutt (1984),Taylor (1985) and Bhaduri and Marglin (1990). The crucial role played by the functional dis-tribution of income in the determination of both consumption and investment in these modelshas given rise to the concepts of wage- and profit-led demand regimes, depending on whicheffect dominates.

Based on these ideas, empirical investigations of the overall effect of redistributing to-ward wages for different countries, time periods or specifications of demand and distributivevariables have yielded contradicting results. Estimations of full macro models tend to showprofit–led demand regimes (Franke, Flaschel, and Proaño, 2006; Chiarella, Franke, Flaschel,and Semmler, 2004; Barbosa-Filho and Taylor, 2006). However, more recent studies havehighlighted the role of the wage share in determining the level of competitiveness and thetrade balance, concluding that demand tends to be profit–led with trade, even if domesticdemand—consumption vs. investment—is wage–led (Bowles and Boyer, 1995; Naastepadand Storm, 2007; Ederer and Stockhammer, 2007; Hein and Vogel, 2008).

This paper extends the short-run Neo-Kaleckian framework to address a different kindof bias in such empirical and theoretical arguments: the size distribution of income. Asthe evidence presented in Piketty and Saez (2003) and below highlights, rising inequality inthe United States in the recent decades has been characterized by an increase in the shareof income held by the top wage earners in addition to a falling wage share. One possible

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approach to this problem, taken by Dutt (1992), Lavoie (1996), and Tavani and Vasudevan(2012), is to add an unproductive managerial class to the basic Kaleckian framework andexamine the effects of wage inequality between managers and workers. Indeed, by alsoendogenizing the functional distribution of income and wage inequality itself, the authorsfind that redistribution toward workers leads to a decline in both inequality and the degree ofcapacity utilization.

This paper has a similar motivation, but follows a different strategy. Instead of addinga third class to the Kaleckian framework, we provide both an empirical and a theoreticalexplanation for the savings rate to be an increasing function of wage inequality. Based onthis extension, we ask two main questions: (i) how has this increase in the top share ofincome affected aggregate demand for a given level of the wage share? and (ii) did thisincrease contribute to the weak response of consumption to the wage share, thus turning thedemand-regime more profit-led?

In an attempt to answer these questions, the paper organizes as follows. First, based onstylized facts regarding the relationship between savings rates and income inequality in theUnited States, Section 2 extends the standard Neo-Kaleckian model to account for differentsize distributions of wage income. While greater inequality necessarily reduces aggregatedemand, we show that the effect of inequality on the demand regime of the economy dependson various parameters due to multiplier effects. Second, in Section 3, we present an econo-metric study examining the role of income inequality in determining the demand regime forthe United States from 1967 to 2010. We find that the increase in inequality after 1980 hasmade the economy more profit-led.

2 Macroeconomic effects of the size distribution of income

2.1 Empirical MotivationMost Neo–Kaleckian models assume that savings rates are different for different incomeclasses. While this assumption is plausible, it is usually taken at face value without presentingempirical evidence. In this section we present such evidence for the US economy. In doingso, we use data for the quintiles of income before taxes from the Consumer ExpenditureSurvey as provided by the Bureau of Labor Statistics.1

In Figure 1 we report the savings rates for each quintile of income after taxes. We com-puted these by calculating (1−C/Y ), where C is the average annual expenditure and Y isthe average annual income of each quintile. Savings rates increase strongly with income.Whereas the top 20% saved about 40 % of their income in 2005, the middle 20% saved lessthan 10% and the bottom 20% borrowed to finance a substantial part of their expenditure.Distribution of income clearly matters for aggregate saving.

The negative values observed for the lower quintiles show the importance of private debtaccumulation in financing household expenditures in the US economy over the reported pe-riod. It is interesting to note that as the top 20 % started to concentrate more of the totalincome after taxes (as shown in Figure 2 below and discussed in Palma (2011)), their average

1Tables from 1984 to 2010 are available at http://www.bls.gov/cex/.

2

Figure 1: Savings rate per income quintile in the United States (1985-2010)

Figure 2: Income share per income quintile in the United States (1985-2010)

savings rate has also increased. A common feature throughout all income quintiles is thejump in savings rates after 2000, possibly showing the private sector’s effort to de-leverage.

The distribution of income in the US economy has become more unequal over the past30 years. Figure 2 presents the share of income after taxes held by each quintile for selectedyears. The figure shows how unequally income is distributed and how this inequality hasbeen rising in the United States. Almost half of total income is held by the richest 20% in2010. These two observations serve as the main motivations for the theoretical and empiricalanalysis that follows.

The stylized facts have two main implications. First, as long as the paradox of thrift holds,an increase in the average savings rate as caused by a rise in income inequality betweendifferent categories of workers necessarily leads to lower aggregate demand. Second, theassumption of differential savings within the category of wage earners is clearly justified and

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needs to be accounted for in the conventional analysis of the relationship between changes infunctional distribution of income and aggregate demand.

2.2 Theoretical argumentMost neo-Kaleckian models restrict themselves to differences in the saving behavior out ofdifferent sources of income. Their focus lies on the distribution between wages and prof-its, the functional income distribution.2 We find this surprising as these models can easilyincorporate personal income inequality. We proceed by presenting an intuitive explanationof how income inequality affects the macroeconomy; a detailed application using a specificfunctional form for the saving function and a Pareto distribution of income is relegated toAppendix A.

Aggregate income is determined by independent investment and consumption/saving de-cisions. We retain the Steindlian-Kaldorian formulation for the investment function, in whichinvestment I depends positively on the rate of capacity utilization u and on the rate of profitr, as well as on the autonomous component γ0 representing so-called "animal spirits". Wemodify the saving function Sw such that the propensity to save out of wages sw now dependson the size distribution of income among workers, captured in the inequality measure σ .The more unequal the distribution, the higher σ and the higher the overall saving propensity:s′w > 0. With this small, but important modification we can state the model equations. Weuse the model presented in chapter 5 of Taylor (2004)3.

gi =IK

= γ0 + γuu+ γrr = γ0 +(γu + γπ(1−ψ))u (1)

gsw =

Sw

K= sw[σ ] ψ u

gsπ =

Sπ

K= sπ π u = sπ (1−ψ) u

With macroeconomic balance between savings and investment requiring that

u = gi−gsw−gs

π = 0. (2)

Substituting equations (1) into (2), we obtain the standard expression for short-run equi-librium output

u∗ = u|u=0 =γ0

−(γu + γπ(1−ψ)− sw[σ ] ψ − sπ (1−ψ))=

γ0

−∆> 0.

Output is determined by autonomous investment, γ0, times the multiplier, ∆. We assumethat the Keynesian stability condition holds, i.e. du

du = ∆ < 0.

2As mentioned in the introduction, one exception are models which incorporate a third class to the model torepresent managers in the form of unproductive labor.

3As in Taylor (2004), all variables will be given as ratios of the capital stock K. The rate of capacityutilization u will be approximated by the output-capital ratio by assuming that capital productivity, namely theratio of potential output to capital, is constant.

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Inequality affects the economy’s overall saving decisions. As wage income is redis-tributed from low- to high-saving classes, leakage increases and aggregate demand falls asone would predict under the Paradox of Thrift. Put formally, this implies

du∗

dσ=

γ0

∆2d∆

dσ=−u∗

ψ

−∆

dsw[σ ]

dσ< 0. (3)

It is clear that redistribution among wage earners always stimulates demand and increasesoutput. This effect is represented by a shift from point A to B in Figures 3 and 4.

The usual debate on redistribution focuses on functional income redistribution, assumingequal distribution within factors. While this assumption might be innocuous for profit earners,the empirical evidence presented in section 2 demonstrates clearly that this does not hold forwage earners. Moreover, the assumption of unequal distribution of wages affects the responseof output to the functional income redistribution, i.e. the demand regime. The demand regimeof an economy is defined as

du∗

dψ= u

1−∆

((sπ − sw[σ ])− γπ)≶ 0. (4)

If an increase in the wage share increases capacity utilization, the economy is said to be’wage-led’, if the opposite holds the economy is considered ’profit-led’. In this model, it isclear from expression (4), that the economy is wage-led if the saving differential betweencapitalists and workers (sπ− sw) is large and investment responds weakly to lower profitabil-ity as represented by a low γπ . The first effect of functional income distribution decreasesoverall leakage in the economy, the second effect prevents injections to fall as ψ increases.

Personal income distribution influences saving out of wages, it thereby also affects thedemand regime of the economy, a feature that has received much attention over the past 20years ((Bowles and Boyer, 1995; Taylor, 2004; Barbosa-Filho and Taylor, 2006; Chiarella,Franke, Flaschel, and Semmler, 2004; Franke, Flaschel, and Proaño, 2006; Ederer and Stock-hammer, 2007; Hein and Vogel, 2008)). Basic intuition tells us that an increase in inequality,caused by a rising share of income held by the top wage earners, increases the average savingout of wage income. This weakens the positive demand effects of a functional income redis-tribution, namely the fall in leakages. However, the changes in the savings rate also reducesthe multiplier and capacity utilization with more subtle effects on investment and saving and,overall, ambiguous effects on the demand regime. To see this more clearly, we differentiatethe expression (4) with respect to σ

d du∗dψ

dσ=− u

(−∆)

dsw

dσ− du∗

dψ

1(−∆)

dsw

dσ≶ 0. (5)

The first term in the inequality captures the immediate effect of saving out of wages on thedemand regime: higher functional income inequality increases saving out of wages, whichlowers the differential between saving out of profits and out of wages. Higher inequalitypushes the demand regime toward more ’profit-ledness’. However, there are repercussionsthrough the effect of inequality on the multiplier (saving and investment behavior). Thismechanism is captured in the second term of the inequality in (5). This term depends on (andtakes the sign of) the demand regime itself and is positive when the economy is wage-led andnegative otherwise.

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Figure 3: Response of aggregate demand to a reduction in wage inequality in the wage-ledcase

Hence, while egalitarian policies of income redistribution always increase capacity uti-lization in this model, their effect on the demand regime of the economy is ambiguous. Ifthe economy is wage-led, redistribution always pushes the economy toward wage-ledness,as represented in Figure 3. This holds also true if the economy is "weakly profit-led". Onlyif the economy is "strongly profit-led" (strong investment responds to profitability and lowfunctional saving differentials), personal income equality leads to more profit-ledness. Theambiguous change in the slope of the demand curve following a reduction in inequality in theprofit-led scenario is represented in Figure 4, giving rise to different responses to an exoge-nous increase in the wage share (points C and D).

Barbosa-Filho and Taylor (2006) found that the US economy is profit-led. In this case,sole theoretical considerations cannot identify the effect of personal wage income inequalityon the US economy’s demand regime. In the next section we reestimate their model account-ing for personal income inequality to inform this question empirically.

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Figure 4: Response of aggregate demand to a reduction in wage inequality in the profit-ledcase

3 Empirical analysis

3.1 Methodology and DataOne of the main difficulties in estimating demand regimes lies in a potential endogeneityproblem between measures of aggregate demand and income distribution. Indeed, as ad-dressed by the literature focused on Goodwin cycles (Goodwin, 1967), income distributionnot only affects, but may also be affected by aggregate demand if lower unemployment leadsto an increase in the power of bargaining of workers. Two main approaches to address thisproblem can be found in the empirical literature. The first has involved the use of instrumen-tal variables to control for each of the two directions of causality (see for instance Nikiforosand Foley (2012)). The second has been to estimate a system of dynamic equations simulta-neously in a Vector Autoregression (VAR) or a Vector Error Correction (VEC) model, thustaking both directions of causality into account. The latter approach was the one used inBarbosa-Filho and Taylor (2006), who by means of a two-dimensional VAR model for ca-pacity utilization and the wage share have found demand in the United States to be profit-led.Based on these results, the empirical study done in this section will investigate the role ofincome inequality in determining such demand regime by making use of a similar method: atwo-dimensional Threshold Vector Autoregression (TVAR).

The idea of the threshold autoregressive model first developed by Tong (1990) is to allowfor a non-linearity in the dynamic relationship that is estimated. In other words, a thresholddefined by the level of a certain variable is searched so as to minimize the sum of squaredresiduals and the estimated coefficients are different in the so-called low and high regimes.The regime-switching (threshold) autoregressive model was extended to the multivariate con-

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text by Tsay (1998), giving rise to the Threshold Vector Autoregressive model (TVAR).4Atwo-dimensional TVAR will be estimated for the degree of capacity utilization and the laborshare, using a measure of the size distribution of income as the threshold variable. In otherwords, the model allows us to investigate whether the level of income inequality affects theresponse of aggregate demand to the functional distribution of income.

The quarterly series for the degree of capacity utilization was calculated as the ratio be-tween actual output (obtained from the Bureau of Labor Statistics) and potential output.5

The series for the labor share is also provided from the Bureau of Labor Statistics at quarterlyfrequency. Both series will be used in logarithmic form in the estimations. Finally, incomeinequality will be measured by the Gini Coefficient provided by the U.S. Census Bureau(2010)6 from 1967 to 2010 annually. The conversion from annual to quarterly data was madeby cubic interpolation.

A two-dimensional TVAR for the labor share and capacity utilization (in logarithmicform) was then estimated using two lags and the Gini coefficient as a threshold variable(lagged by one period), for the period 1967-2010. The threshold value was selected au-tomatically based on a grid search which minimized the sum of squared residuals of thecorresponding estimation.7

Linear accumulated impulse response functions to Cholesky standard deviation innova-tions were computed for the two regimes separately using the corresponding coefficients andthe residuals of each TVAR8.

3.2 ResultsThe results of the TVAR estimation for the period 1967-2010 are presented in Table 1 inthe Appendix. The selected threshold for the Gini coefficient determining the low and highinequality regimes was 0.406, which corresponds to the value attained in 1981. The low(high) inequality regime, which comprises 32.9% (67.1%) of the total of observations, thuscorresponds to the years before (after) 1981. Both regimes are shown to be characterizedby profit-led demand, with the total effect of the labor share Ψ in the equation for capacityutilization u being negative even if it is positive for the first lag (due to higher consumption).

Figure 5 presents the accumulated response of the degree of capacity utilization to astandard deviation shock in the labor share for the low and high inequality regimes9. Thefigure shows that in the high inequality regime the impact of an increase in the wage sharein capacity utilization is more negative. In other words, results of the TVAR suggest that the

4Different types of models have been developed to address non-linearities in time series since Tong’s originalthreshold autoregressive model. See Hansen (2011) for a survey of such developments applied to economics.

5As in Barbosa-Filho and Taylor (2006), the series for potential output was derived from the output seriesusing a Hodrick-Prescott filter.

6Current Population Survey, Annual Social and Economic Supplements, available athttp://www.census.gov/hhes/www/income/data/historical/household/h04.html

7The R program is available from authors upon request.8Since exogenous shocks may generate a switch from one regime to the other, generalized non-linear impulse

response functions based on initial conditions are developed in Koop, Pesaran, and Potter (1996), but will notbe estimated here.

9The impulse response functions for the other direction of causality – the effect of aggregate demand ondistribution – are presented in the appendix but will not be analyzed here.

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Figure 5: Accumulated impulse response function of the degree of capacity utilization to astandard deviation shock in the labor share in the low and high inequality regimes for theUnited States (1967-2010)

increase in income inequality has turned demand more profit-led in the United States overthis period. Hence, these results seem to confirm the theoretical argument presented in theprevious section which corresponds to the weakly profit-led case.

4 DiscussionIncome distribution has become more unequal in the past decades, reversing much of thegains from post-WWII. This holds true for shifts toward profits in the functional incomedistribution and shifts toward high-income earners within wage income. While these shiftshave gained the attention of the wider public through the ’Occupy Wall Street’ movement, theacademic debate has focused almost exclusively on the impact of changes in the functionalincome distribution.

Empirical evidence clearly shows that wage earners have different saving rates dependingon the disposable income. Saving rates rise from negative for the bottom 20% to as highas 40% for the top 20% in the year 2010. Given these differences in saving behavior, weanalyze the effects of recent increases in wage income inequality on aggregate demand andthe economy’s demand regime.

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While the Paradox of Thrift predicts that output falls as inequality rises, the effects ofchanges in the functional income distribution on output under different wage income dis-tributions is ambiguous. Higher wage equality makes the economy more wage-led. If theeconomy is profit-led, the sign of this effect is ambiguous and depends on the level of de-mand regime itself. These nonlinear effects in the IS curve complements recent work on non-linearities by Nikiforos and Foley (2012) who present empirical evidence for a non-lineardistribution schedule.

Since our theoretical model cannot clearly identify the effects of wage income inequal-ity on the demand regime, we proceed empirically by estimating a non-linear version of themodel by Barbosa-Filho and Taylor (2006) in order to determine the effect of income in-equality on the demand regime for the post-WWII US economy. The linear estimation by theauthors had suggested that the US economy is profit-led. Our estimations show the US mayhave become more profit-led in times of high inequality.

These findings add to recent evidence that the standard Kaleckian model incompletelycaptures interactions between demand and distribution when applied to today’s advancedeconomies: Dutt (2006) extends the model to account for consumer debt, Rezai (2011) andvon Arnim, Tavani, and de Carvalho (2012) highlight the importance of open-economy is-sues. We introduce personal income distribution as a third omitted and potentially importantbias.

Our results have clear and important implications for economic policy. As the GreatRecession keeps unfolding and the political climate shifts increasingly against traditionaleconomic stimuli to prop up demand, taxes-and-transfer schemes can proof effective. Whilethe demand effects of increases in money wages might be repressed by concurrent increasesin inflation under mark-up pricing rules, the demand effect of redistribution from profits to-ward wages depends on the economy’s demand regime. Our findings suggest that egalitarianpolicies within wage earners increase demand irrespective of such considerations. Loweringwage income inequality always increases aggregate demand due to the Paradox of Thrift.Moreover, lowering inequality among wage earners can, and in fact in the US economy does,tilt the economy in a wage-led direction, providing arguments for progressive and expansion-ary policy in the form of redistribution in functional income on economic – rather than meresocial – grounds in the future.

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AppendixA An application of the modelIn this section we present the derivation of the aggregate saving function for an economyin which wage income follows a Pareto distribution. We pick the Pareto distribution fortwo reasons: first, since income cannot be negative, the probability density function needsa lower limit under which it has measure 0. This limit is defined as parameter k for thePareto distribution. Second, Yakovenko (2012) demonstrates that the distribution of personalincome in the US exhibits a ’fat’ tail. The Pareto distribution has such a fat tail.

Let personal income equal y > κ , then the probability density function (pdf) of a Paretodistribution is

f (y) =k α

yα−1 if κ ≤ y

0 if κ > y

The median, µ , and median, ν , of a Pareto are defined as

µ =κ α

α−1for α > 1 and ν = 21/α

κ.

We assume that personal saving decision of household i depends the income of householdi, yi, and the income of the median household, yν . Household i’s saving is defined as

Si = a0 yi +a1(yi− yν).

Aggregate saving is the sum of all saving:

Sw =∫

[a0 yi +a1(yi− yν)] f (y) dy = a0 µ +a1(µ−ν) =

[a0 +a1(1−

ν

µ)

]µ.

µ eqals average income, which has to be related to the macro variables of the Kaleckianmodel of section 2. Average income times population size has to equal aggregate wageincome: µ L≡ ψ X or µ ≡ ψ u k. A Pareto distribution has 2 degrees of freedom, κ and α .We use κ to ensure that the identity is satisfied,

κ ≡ α−1α

ψ u k.

Normalizing population size to 1, L ≡ 1, and substituting this expression into the savingfunction, we obtain a saving function of the form used in our theoretical model

Sw

K=

[a0 +a1(1−

21/α α−1α

)

]ψ u = sw [α] ψ u.

with sw [α] the average propensity to save (APS). The second parameter of the Paretodistribution, α , captures the degree of wage income inequality. As α increases, more incomeis concentrated at the bottom and the more equal wage income distribution.

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sw [α] has both properties used for the comparative statics used in section 2: first, aver-age aggregate saving falls as the economy becomes more equal and, second, under equallydistributed income, the analysis conflates to the traditional assumption of a constant APS:

dsw

dα< 0

limα→∞

sw → a0

Our results therefore hold for specific (and realistic) assumptions on the distribution ofincome across wage earners.

B Econometric results

Figure 6: Accumulated impulse response function of the labor share to a standard deviationshock in the degree of capacity utilization in the low and high inequality regimes for theUnited States (1967-2010)

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Equation for u Equation for Ψ

Low Inequality High Inequality Low Inequality High Inequalityu−1 1.3095*** 1.4477*** -0.0039 0.0732u−2 -0.5941*** -0.6297*** 0.2071* 0.0948Ψ−1 0.8536*** 0.2956** 0.5271*** 0.7473***Ψ−2 -0.9124*** -0.3181** 0.1603 0.2652**Intercept 0.2456 0.0932 1.3061*** -0.053Signif. Codes: *** 1%; **5%; *10%Threshold value: 0.406469Percentage of Observations in each regime: 32.9% 67.1%

Table 1: Results of the two-dimensional TVAR estimation for the United States (1967-2010)using the Gini Coefficient as a threshold.

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